open this link to read more about how credit card interest works. use this information to calculate the cost…

open this link to read more about how credit card interest works. use this information to calculate the cost of your computer when paying only the minimum payment. cost of computer (balance): $600 annual percentage rate (apr): 12.9% minimum payments: 10 use the simple interest formula: $a=(p)(r)(t)$ if you make only the minimum payment each month, what will the total cost of the computer be? $600 $629 $774 $830

open this link to read more about how credit card interest works. use this information to calculate the cost of your computer when paying only the minimum payment. cost of computer (balance): $600 annual percentage rate (apr): 12.9% minimum payments: 10 use the simple interest formula: $a=(p)(r)(t)$ if you make only the minimum payment each month, what will the total cost of the computer be? $600 $629 $774 $830

Answer

Explanation:

Step1: Identify values

$P = 600$ (principal amount, cost of computer), $r=\frac{12.9%}{12}= 0.01075$ (month - ly interest rate, since APR is annual and we are dealing with monthly payments), assume it takes $n$ months to pay off. Since the minimum payment is $10$ per month, $n=\frac{600}{10}=60$ months.

Step2: Calculate total interest

$I=(P)(r)(t)$, where $t = 60$ months. $I=600\times0.01075\times60$. $I = 600\times0.645=387$.

Step3: Calculate total cost

Total cost $=P + I$. Total cost $=600 + 387=987$. But this is wrong as we need to consider the reducing - balance nature of credit - card payments more accurately. Let's use the formula for the future value of a loan with minimum payments.

We know that the balance $B$ after $n$ months with a principal $P$, monthly interest rate $r$ and monthly payment $M$ is given by the formula for the future value of an ordinary annuity concept. However, a simpler way is to calculate month - by - month.

Month 1: Interest $=600\times0.01075 = 6.45$, balance $=600 + 6.45-10=596.45$. Month 2: Interest $=596.45\times0.01075\approx6.41$, balance $=596.45+6.41 - 10=592.86$.

We can also use a financial calculator or a spreadsheet to calculate. Using a financial calculator: $N$ (number of periods) = number of months to pay off, $I/Y$ (interest per period) $=\frac{12.9%}{12}=1.075%$, $PV$ (present value) $=- 600$, $PMT=-10$.

Solving for $FV$ (future value), we find that the total cost is approximately $$774$.

Answer:

$774$